On the Possibility of Generalizing the Results of Studies of Dynamical Systems on the Example of a Vehicle Suspension

Abstract

The dynamics of mechanical systems, the operation of electromagnetic and electronic devices and devices, the principle of operation of a number of machines and mechanisms, engineering structures from various fields are often described by differential equations and their systems. Differential equations are often mathematical models of the movement and operation of various engineering objects. As a rule, such equations are solved by numerical methods for specific parameter values. These methods of solving differential equations are widely used in practice. However, these methods also have significant disadvantages. For example, the solution of differential equations is obtained for a specific object with the specified parameters. In this case, a solution is obtained for a single point in the parameter space of a set of similar objects, points in this space of the considered family of objects. A natural question arises: Is it possible to extend the results of the solution for a single point in space (a specific object) and the identified properties and regularities to other points (other objects) of the considered family? The purpose of this article is to identify conditions under which it is possible to generalize the results of solving differential equations with specific parameter values describing a single construction to the entire family of similar constructions, the entire space of parameters under consideration. The implementation of the identified conditions is illustrated by the example of solving the problem of “analyzing the dynamic properties of a mathematical model of a car with adaptive (adjustable) suspension of a new principle of action (developed by the authors), moving at a variable speed along an indirect profile of the road surface and developing recommendations for their radical improvement”.